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TechnologyCelestial NavigationObservations at the Kansas River
Approximating Longitude
Longitude & Declination
 

Chronometer Error

Page 4 of 7

Local Time

eridian Altitude observations of the sun could be taken without the need of a timepiece; most all other celestial observations were dependent on knowing the correct Local Apparent Time to within a few seconds. To take the meridian altitude of the sun, the observer watched the progress of the sun as it neared its daily apex, then, sighting with the octant or sextant, ďtrackedĒ it. The sun hangs for a few moments at its highest altitude before descending. At this point the observer locks the index arm in place, then reads the angle observed. This is the sunís meridian altitude above the horizon.

Local Apparent Time is the time as shown by the sun at your location. When it is Local Apparent Noon the sun is due south of you, which is to say, on your meridian, and is (for all practical purposes) at its highest point in the sky. The time given by the chronometer for Local Apparent Noon, after a correction made for the sunís changing declination and subtracted from 12:00:00, gives the error of the chronometer on Local Apparent Time for that particular noon. This time-check observation was called an ďEqual Altitudes Observation of the Sun.Ē

Lewis took his Equal Altitudes observations as follows:

1) He set out the artificial horizon.
2) When the sun was nearly east or rising rapidly and had reached an altitude high enough to reduce the effects of refraction, he measured the altitude of the sunís upper limb ó that is, the upper edge of its disk ó with the sextant and, simultaneously, had an assistant note and record the time shown by the chronometer. He then locked the index arm at the angle observed,
3) Leaving the index arm locked at the angle observed, he called out to his assistant when the sunís center reached that altitude. The assistant noted and recorded the time.
4) When the sunís lower limb reached that same altitude Lewis again called out to his assistant to note and record the time.
5) Lewis then verified the altitude shown by the sextantís index, recorded that altitude, then put the sextant away until the afternoon sun descended nearly to the altitude of the morning measurements.
6) As the afternoon sunís lower limb, center, and upper limb successively reached the altitude locked on the sextantís index arm, Lewis called out to his assistant to note and mark the time.

From these data, the time that the chronometer would have shown at local noon could be calculated to within a second or so of noon ó depending upon the accuracy of the observation. From observations taken the next day or a few days later, the chronometerís daily and hourly rate of loss could be determined. Lewis and Clark took Equal Altitudes observations of the sun on the July 27, 28and 29 to determine their chronometerís error with respect to local time. These observations also provided the necessary information to determine the chronometerís going rate (for Lewisís chronometer this meant how much time the chronometer lost per day). Although the captains did not calculate the chronometerís error while at the mouth of the Kansas River, Lewis would need to make these calculations to determine the magnetic declination and the longitude from the other observations he and Clark took there. The Equal Altitudes observations taken during those three days yield the following information:

Chronometer Error

The difference of two seconds in the chronometerís daily rate of loss does not necessarily reflect any change in its rate of loss at this location. It likely stems from the inaccuracy of the Equal Altitudes observations, themselves. The average daily loss of 21.4 seconds, however, certainly is significantly greater than the 15.5 seconds per day that Lewis recorded on July 22, 1804.1

--Robert N. Bergantino, 06/06

1. Moulton, ed., Journals, 2:412.

Funded in part by a grant from the National Park Service, Challenge-Cost Share Program.

Approximating Longitude
Longitude & Declination


 
From Discovering Lewis & Clark ®, http://www.lewis-clark.org © 1998-2014
by The Lewis and Clark Fort Mandan Foundation, Washburn, North Dakota.
Journal excerpts are from The Journals of the Lewis and Clark Expedition, edited by Gary E. Moulton
13 vols. (Lincoln: University of Nebraska Press, 1983-2001)